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jimmy m
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07 Nov 2020, 2:48 pm

Three scientist discovered a simple formula that, if true, established an unexpected relationship between some of the most basic and important objects in linear algebra. The physicists — Stephen Parke of Fermi National Accelerator Laboratory, Xining Zhang of the University of Chicago and Peter Denton of Brookhaven National Laboratory — had arrived at the mathematical formula while grappling with the strange behavior of particles called neutrinos. They’d noticed that hard-to-compute terms called “eigenvectors,” describing, in this case, the ways that neutrinos propagate through matter, were equal to combinations of terms called “eigenvalues,” which are far easier to compute. Moreover, they realized that the relationship between eigenvectors and eigenvalues — ubiquitous objects in math, physics and engineering that have been studied since the 18th century — seemed to hold more generally.

Source: Neutrinos Lead to Unexpected Discovery in Basic Math


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magz
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07 Nov 2020, 2:54 pm

The identity is not exactly new:
https://arxiv.org/abs/1908.03795

Quote:
In this survey we describe the many times that this identity, or variants thereof, have been discovered and rediscovered in the literature (with the earliest precursor we know of appearing in 1834).
The thing seems, it's not widely known despite being simple and likely useful.


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Fnord
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07 Nov 2020, 2:55 pm

jimmy m wrote:
... They’d noticed that hard-to-compute terms called "eigenvectors", describing, in this case, the ways that neutrinos propagate through matter, were equal to combinations of terms called "eigenvalues", which are far easier to compute. Moreover, they realized that the relationship between eigenvectors and eigenvalues -- ubiquitous objects in math, physics and engineering that have been studied since the 18th century -- seemed to hold more generally...
Merely a confirmation of previously-understood principles, much the same as Tensor Transforms being related to Tensor Values -- nothing more.